Volume 9, Issue Supplement 2, September 2002, Pages 122 - 133
Should PT Symmetric Quantum Mechanics Be Interpreted as Nonlinear?
Received 1 March 2002, Available Online 2 September 2002.
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The Feshbach-type reduction of the Hilbert space to the physically most relevant "model" subspace is suggested as a means of a formal unification of the standard quantum mechanics with its recently proposed PT symmetric modification. The resuting "effective" Hamiltonians Heff (E) are always Hermitian, and the two alternative forms of their energy-dependence are interpreted as a certain dynamical nonlinearity, responsible for the repulsion and/or attraction of the levels in the Hermitian and/or PT symmetric cases, respectively. The spontaneous PT symmetry breaking is then reflected by the loss of the Hermiticity of Heff while the pseudo-unitary evolution law persists in the unreduced Hilbert space.
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Cite this article
TY - JOUR AU - Miloslav Znojil PY - 2002 DA - 2002/09/02 TI - Should PT Symmetric Quantum Mechanics Be Interpreted as Nonlinear? JO - Journal of Nonlinear Mathematical Physics SP - 122 EP - 133 VL - 9 IS - Supplement 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2002.9.s2.11 DO - 10.2991/jnmp.2002.9.s2.11 ID - Znojil2002 ER -